It's an interesting open question what we would want to replace intellectual property with.

My brain is so used to capitalism that I would be inclined to preserve things like artists having a contractual obligation to turn their work into a finished product if they got paid for it by someone that wanted a finished product. But if you look at some of the great renaissance artists, many of them were infamous for just skipping town and leaving unfinished works left and right when they got bored of making them. So maybe it's better to just accept that many great works are never finished so that other, greater works can get made instead.

One thing that does seem very important is crediting the actual artists and people that made it possible. Not to deny the right to copy or distribute, but to make it so people just know who is responsible and who they want to support or praise or communicate with. You would need infrastructure for that to make it easy to check, to remove duplicates, and to make sure entries give credit correctly.

Another important thing is the location, maintenance, and integrity of physical pieces. Hoarding seems bad, especially behind closed doors and especially without the permission of the creator or their (cultural) descendants. Letting artpieces decay seems bad, especially if others would pay to maintain them. Defiling artpieces seems bad, perhaps even with the creator's consent. But how do we decide which measures, if any, are okay to address these issues? I honestly don't know.

I don't know if it's necessary to do anything beyond these two that is specific to art. As long as there is a digital currency and wealth is already fairly distributed, voluntary patronage and donations (using the crediting infrastructure to make sure it ends up at the right places) may just be the best system for deciding which artists get what budget and how much of the world's resources and labor go to art. If wealth weren't fairly distributed, poor people would have less say in what gets made than everyone else, but the solution to that is to redistribute the wealth, not to patch that up with special rules for art. If there is no digital currency, then it's inconvenient to pay artists remotely.